Steradian

The steradian, also steradian is a unit of the solid angle. In the SI unit system it is included as a derived unit. The unit symbol for the steradian sr.

On a sphere of 1 m radius a steradian encloses an area of ​​1 m² on the ball surface. The solid angle of the surface of a sphere is 4π sr.

Definition

Given a sphere of radius. Then a steradian solid angle of the saw from the middle of the ball of a spherical segment occupies the area on the spherical surface. This solid angle can be calculated as the area of the spherical cap divided by the square of the radius:

The division means that the solid angle is independent of the radius of the examined ball.

Solid angle of a cone, the cut out part of a surface ( ) of 13.5 m² of a sphere with a radius of 3 m is.

Refers to the solid angle of a circular cone from the center of the sphere, as shown in the figure on the right ( canonical solid angle ), so you can look at it in a section through the center of the sphere as a flat angle. From the relationship of the area of ​​the spherical cap of the cone angle and the following relationship can be derived:

The opening angle of a cone, which covers the solid angle 1 SR, is about 65.54 °.

Historical

In the SI was initially left open whether steradian and Radiant are derived units or base units; for both was the class of " supplementary units " created. 1980 recommended the CIPM to interpret these additional units as derived. This was followed in 1995 the 20th CGPM and decided in Resolution 8, the abolition of class of supplementary units.

The unit symbol " sr " has been defined by the CIPM in 1950. Previously, the characters " st " and " steradian " were used.